Softmax Function

Softmax is one of the most important functions for neural networks. It also has some interesting properties that we list here. This function is part of The Exponential Family, one can also see that the sigmoid function is a particular case of this softmax, just two variables. Sometimes this could be seen as a relaxation of the action potential inspired by neuroscience (See The Neuron for a little bit more about neurons). This is because we need differentiable, for gradient descent. The action potential is an all or nothing thing. ...

3 min 路 Xuanqiang 'Angelo' Huang

The Exponential Family

This is the generalization of the family of function where Softmax Function belongs. Many many functions are part of this family, most of the distributions that are used in science are part of the exponential family, e.g. beta, Gaussian, Bernoulli, Categorical distribution, Gamma, Beta, Poisson, are all part of the exponential family. The useful thing is the generalization power of this set of functions: if you prove something about this family, you prove it for every distribution that is part of this family. This family of functions is also closely linked too Generalized Linear Models (GLMs). ...

6 min 路 Xuanqiang 'Angelo' Huang

Transliteration systems

This note is still a TODO. Transliteration is learning learning a function to map strings in one character set to strings in another character set. The basic example is in multilingual applications, where it is needed to have the same string written in different languages. The goal is to develop a probabilistic model that can map strings from input vocabulary $\Sigma$ to an output vocabulary $\Omega$. We will extend the concepts presented in Automi e Regexp for Finite state automata to a weighted version. You will also need knowledge from Descrizione linguaggio for definitions of alphabets and strings, Kleene Star operations. ...

4 min 路 Xuanqiang 'Angelo' Huang

Bag of words

Bag of words only takes into account the count of the words inside a document, ignoring all the syntax and boundaries. This method is very common for email classifications techniques. We can say bag of words can be some sort of pooling, it鈥檚 similar to the computer vision analogue. It鈥檚 difficult to say what is the best method (also a reason why people say NLP is difficult to teach). Introduction to bag of words Faremo una introduzione di applicazione di Na茂ve Bayes applicato alla classificazione di documenti. ...

2 min 路 Xuanqiang 'Angelo' Huang